Modify either Campaign or Ingroup (depending on whether the call in question was inbound or outbound).
In both of those Modify views there are fields for "Dispo URL" and other URLs as well. But you want Dispo URL. This field allows you to send ALL the data from the call to any web server you like.
Danger: If you put a web page in now and some day that web server goes offline, it may back your server up horribly. Be sure to delete dead links.
There are some samples in /agc/ for what can be done with the dispo url. dispo_move_list.php & dispo_send_email.php are good for understanding.
and Thank You
for posting your specs!